Suggestions for Base and Rings for Rem 700 LA

I need to get my newly acquired Leupold VXII 3-9x40 mounted on my Rem 700 in .338 WM. This is more of a medium range rifle (<500 yards. I have a 7mm RUM for the longer stuff), hence the 3-9x. I am planning on using the Burris Signature mounts because I have had great luck with them on some of my other rifles. But, I'm kind of stuck on which base to get. Should I get one of the picatinny rails? I think this would give me the most options. Also, if I do go with the picatinny, should I go 1pc or 2?

Also, this gun is stainless, and the scope is silver. So I'd like to keep that scheme going. I can paint if I need to.

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